Suppose a mechanical oscillator has movement denoted by $y$ and we have a particular solution to the differential equation $y'' + cy' + 4y = \cos(\omega t)$ as $y(t) = \frac{4}{\sqrt{(\omega^2 - 4)^2 + \omega^2}}\cos(\omega t - \phi)$
Find the value of $\omega$ for which (if) any resonance is created.
So I understand that resonance is where the amplitude is the maximum, so we have to maximize
$\displaystyle f(\omega) = \frac{4}{\sqrt{(\omega^2 - 4)^2 + \omega^2}}$
I got $\omega = \sqrt{7/2}$, but is this right?
Or are we just supposed to solve the denominator for $0$?